Solving the unsolvable: are there questions science will never be able to answer?

Should we accept that there are things about the universe that we may never be able to know?

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For three years I've been on a mission. Usually scientists are on the hunt to extend the boundaries of knowledge and discover the next big thing: gravitational waves; or a new species of animal. But I've been on a different quest. I'm on the search for the things we cannot know. Not the things we don't know now, but to see if there are any questions in science that by their very nature we will never be able to answer one way or the other. Perhaps there aren't any. Perhaps it is possible for us to know it all. Or does science have its known unknowns?

It's always dangerous in science to say you'll never know something. For most scientists, saying something is impossible is like a red rag to a bull. The history of science is stuffed full of tales of people who've claimed we've hit the boundaries of knowledge - only for the next generation to smash the glass ceiling erected by their predecessors.

Take the statement made by French philosopher Auguste Comte in 1835 about stars: "We shall never be able to study, by any method, their chemical composition or their mineralogical structure." Fair enough, given that you'd think that this knowledge would depend on visiting the star. What Comte hadn't factored in was the possibility that the star could visit us - or at least photons of light emitted by it could bring us knowledge of the chemical make-up of stars. A few decades after Comte's prophecy, scientists had determined the chemical composition of our own star, the Sun, by analysing its light spectrum.

In 1900, Lord Kelvin, regarded by many as one of the greatest scientists of his age, believed his peers knew it all: "There is nothing new to be discovered in physics now," he announced. "All that remains is more and more precise measurement." American physicist Albert Abraham Michelson concurred. He too thought the future of science would simply consist of adding a few decimal places to the results already obtained. "The more important fundamental laws and facts of physical science have all been discovered… Our future discoveries must be looked for in the sixth place of decimals."

Five years later, Einstein announced his extraordinary new conception of time and space, followed soon after by the revelations of quantum physics. Kelvin and Michelson couldn't have been more wrong about how much new physics there was still to discover. So isn't it crazy to go out on a limb and risk identifying things that we'll never know? And yet in my own subject of mathematics, one of the greatest breakthroughs of the twentieth century was Kurt Gödel's proof that within any mathematical framework there will be true statements that you cannot prove are true within that system.

So perhaps I can use the same strategy to prove that there are things in science we can never know?

Will it ever be possible to know what happened before the Big Bang? Or can we be sure that we will never know?

Liam Stevens

Here's a question that at first sight appears unknowable: is the Universe infinite? Because the speed of light is finite and information travels no faster than the speed of light, and because the Universe has only been going for 13.8 billion years, there is a bubble surrounding the Earth beyond which we can receive no information. It's like we're living in our own version of The Truman Show, with no possibility of knowing whether or not there is a celestial film crew on the other side of the bubble, looking in on us. So if the Universe is infinite, how could we ever get any information beyond this boundary to let us know?

And yet mathematics has been incredibly effective at allowing us to explore the infinite. We know that if we write the square root of two as a decimal, then it goes on to infinity, never repeating itself. We have never written down this number, but we know it goes on to infinity. Perhaps we can prove the same thing about the Universe even without ever being able to go there. Perhaps a finite Universe just contradicts any model we might propose for the physical laws obeyed by nature. Mathematics is probably our most powerful telescope for looking deep into the night sky.

So if we could possibly answer such a seemingly unknowable question, might it be possible to know it all? Are quarks the last layer as we divide matter? Will we understand what makes a network of neurons conscious? What happened before the Big Bang? In some ways it would be absolutely extraordinary if we could know it all. The Universe is not constructed for our convenience. It's not an exercise in the philosophy of science. Maybe the only thing we can really be sure that we'll neverknow, is what it is we'll never know.

Marcus du Sautoy is professor of mathematics at the University of Oxford and wrote What We Cannot Know (Fourth Estate)

This article was first published in the September 2016 issue of WIRED magazine